Discrete Mathematical Structures, 6/e (IE-Paperback)

Bernard Kolman, Robert Busby, Sharon C. Ross




Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field.

This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.


  • The focus on computer science prepares students for future computer science careers.
  • The emphasis on proof lays the foundation for mathematical thinking.
  • Clear organization of topics prevents students from being overwhelmed. The authors treat relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.
  • Vignettes of mathematical history open each chapter, providing students with a practical background of how these ideas were developed.
  • Additional number theory coverage provides more information on the properties of integers, including base n representations, and gives more contexts for isomorphism.
  • Cryptology is explored throughout the book, introducing students to this exciting field.
  • Coverage of coding provides students with a full picture of all of its aspects, including efficiency, effectiveness, and security. A set of coding exercises for each chapter is also included in Appendix C.
  • Exercises emphasize multiple representations of concepts, and provide practice on reading and writing mathematical proofs.
  • Experiments provide opportunities for in-depth exploration and discovery, as well as for writing and for working in groups. Topics include weighted voting systems, Petri nets, Catalan numbers, and others.
  • End-of-chapter material includes Tips for Proofs, a summary of Key Ideas, and a Self-Test, which contains a set of conceptual review questions to help students identify and synthesize the main ideas of each chapter.

    New to This Edition
  • New sections on Logic, Mathematical Statements, and Logic and Problem Solving help students understand proofs and proof techniques. Additional exercises help students develop conjectures and how to prove or disprove them.
  • More applications, exercises, and figures have been added to help students learn and retain the material.
  • New material on fuzzy sets and fuzzy logic introduces students to a topic that is extremely important for modern issues of automated feedback and control of processes.
  • Popular puzzles like Sudoku and their underlying mathematical connections form a continuous thread in the text, connecting set theory, Boolean matrices, algorithms and coding, logic, the general construction of proofs, coloring problems and polynomials, and other topics in a way that students will find both interesting and instructive.

    Table of Contents
    1. Fundamentals
    2. Logic
    3. Counting
    4. Relations and Digraphs
    5. Functions
    6. Order Relations and Structures
    7. Trees
    8. Topics in Graph Theory
    9. Semigroups and Groups
    10. Languages and Finite-State Machines
    11. Groups and Coding



- 重點放在計算機科學上,為學生未來的計算機科學職業做好準備。
- 強調證明,為數學思維奠定基礎。
- 清晰的主題組織,避免學生感到壓倒性。作者將關係和有向圖視為同一基本思想的兩個方面,然後將其作為幾乎所有在書中介紹的概念的基礎。
- 數學歷史的插圖開啟每一章,為學生提供這些思想是如何發展的實際背景。
- 額外的數論內容提供更多關於整數性質的信息,包括基於n進制的表示法,並為同構提供更多的上下文。
- 書中探討了密碼學,向學生介紹這個令人興奮的領域。
- 編碼的涵蓋範圍為學生提供了完整的圖像,包括效率、效果和安全性。附錄C還包含了每章的編碼練習題。
- 練習強調概念的多重表示,並提供閱讀和撰寫數學證明的練習。
- 實驗提供了深入探索和發現的機會,以及寫作和小組合作的機會。主題包括加權投票系統、Petri網、卡塔蘭數等。
- 章末材料包括證明提示、關鍵思想摘要和自測,其中包含一組概念回顧問題,幫助學生識別和綜合每章的主要思想。

- 新增關於邏輯、數學陳述和邏輯與問題解決的章節,幫助學生理解證明和證明技巧。額外的練習幫助學生發展猜想以及如何證明或反駁它們。
- 增加了更多應用、練習和圖片,幫助學生學習和保留材料。
- 新增了模糊集合和模糊邏輯的新內容,向學生介紹了對於現代自動化反饋和過程控制非常重要的主題。
- 流行的謎題,如數獨及其潛在的數學聯繫,貫穿整本書,將集合論、布爾矩陣、算法和編碼、邏輯、證明的一般構造、著色問題和多項式等主題以學生感興趣和有教育意義的方式相連。

1. 基礎
2. 邏輯
3. 計數
4. 關係和有向圖
5. 函數
6. 順序關係和結構
7. 樹
8. 圖論中的主題
9. 半群和群
10. 語言和有限狀態機
11. 群和編碼